Recent content by bubblesewa

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    Proving Continuity of Derivatives for a Multivariable Function

    Oh, sorry. Yeah. I was talking about the directional derivative. I don't know how to write the actual notation for directional derivatives on here. And thank you for your help!
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    Gradient Vector Proof for Local Minimizer: f(x)=0, Df(x)=0 | R^n --> R

    Is this about what my proof should look like then? And thanks for welcoming me btw. Since x is an interior point of Rn, we can choose a positive number r such that the open ball Br(x) is contained in Rn. Fix an index i with 1 < i < n. Then, do I suppose that I have some function, let's say...
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    Gradient Vector Proof for Local Minimizer: f(x)=0, Df(x)=0 | R^n --> R

    Homework Statement Suppose that the function f: Rn --> R has first-order partial derivatives and that the point x in Rn is a local minimizer for f: Rn --> R, meaning that there is a positive number r such that f(x+h) > f(x) if dist(x,x+h) < r. Prove that Df(x)=0. Homework Equations...
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    Proving Continuity of Derivatives for a Multivariable Function

    Homework Statement Suppose that the function f: R^n --> R is continuously differentiable. Let x be a point in R^n. For p a nonzero point in R^n and alpha a nonzero real number, show that (df/d(alphap))(x)=alpha(df/d(p))(x)Homework Equations A function f: I --> R, defined on an open...